Multi-Strain Host-Vector Dengue Modeling: Dynamics and Control
■135
0.0
4.0
8.0
0
0.5
1.0
0.0
500
1000
0
20
40
60
80
100
TC
V
I
S
β
Figure 6.9: One-parameter diagram for the bifurcation parameter β for the SIRqVM model
(6.15) with qb = 1, qν = 1 and M∞= 1 where using (6.17): βTC = 52.02.
6.5.3
Viability analysis of vector control
In [40] the effect of introducing control through mosquito repellents used in textiles,
paints and other household items (curtains, furniture) in a model for a vector-borne dis-
ease of a susceptible-infected-removed type for the host and susceptible-infected for the
mosquito vector is investigated. Modeling of control measures in the context of vector-
borne diseases has focused on optimal resource allocation [14, 37, 38, 47, 46, 54]. Stability
analysis of epidemiological models investigates the asymptotic convergence of solutions to
equilibria with specific properties, but does not answer the question of transient dynamic
behavior.
a
b
0.0
4.0
8.0
0
0.5
1.0
0.0
500
1000
0
0.2
0.4
0.6
0.8
1
TC
V
I
S
qb
0.0
4.0
8.0
0
0.5
1.0
0.0
500
1000
1
2
3
4
5
6
7
8
9
10
TC
V
I
S
qb
Figure 6.10: One-parameter diagram for the vector control parameter qb for SIRqVM
model (6.15), where qν = 1 and M∞= 1. In panel a β = 104 where qbTC = 0.50 and
in panel b β = 10 where qbTC = 5.20.